2022-09-09 19:24 Status: Tags: [pi filter](pi%20filter.md) # high-pass and low-pass phase shifter ## Tee and Pi Filters ### Configurations  [^1] See [pi filter](pi%20filter.md) and [tee filter](tee%20filter.md). Low pass works well for DC - amplifiers are like bandpass. When combined with phase shifter - needs to operate from DC to this frequency. ## Common Uses Used to implement higher bits (180,90 deg). For lower bits, large inductors and very small capacitors are needed. > This doesn't work as the large parasitic capacitances of a large inductor make the small capacitance impossible to obtain [^common_uses] ## Connection to transmission line ### Equation Derivation Using the [ABCD](ABCD.md) network derived, [^2] matrix for a transmission line, the lumped element L and C values for a given phase shift $\phi$ and configuration (high or low pass [tee](tee%20filter.md) or [pi](pi%20filter.md)) can be determined. An example calculation for a [highpass](highpass%20filter.md) [tee](tee%20filter.md) is:    ## Conventions "the high-pass arm provides the reference state, as it provides the least-negative insertion phase."[^1]  ## Comparison to [switched line filters](switched%20line.md) The filter-based phase shifter can handle larger bandwidths for [phase errors](phase%20errors.md). ### Delay Line   ### Filter Design   [^3] ## Calculation of lumped elements >Below are exact lumped element values for four different bits at 6 GHz (which of course we calculated in a spreadsheet!) You can scale the L and C values as 1/frequency, or make your own spreadsheet, or wait for us to post ours one of these days. Remember that each filter provides half the desired phase shift, i.e. the LP filter for 22.5 degrees provides 11.25 degrees (negative) phase. ## Improving Performance More than 50% of phase shift is performed by the low pass network, for better bandwidth. >"In many real phase shifters you'll find that more than 50% of the phase shift is done in the low pass network and less than 50% in done in the high pass. Why? It just seems to give better bandwidth! That is exactly what is going on in the TGP2104. The series inductors in the LP network are longer than the shunt inductor in the HP network. So the LP network contributes perhaps -135 degrees phase shift while the HP network contributes +45 degrees."  >Did we mention that for the ideal 180 bit calculation, the L's and C's are the same for the HP and LP networks? --- # References [^1]: [High-Pass Low-Pass Phase Shifters (microwaves101.com)](https://www.microwaves101.com/encyclopedias/high-pass-low-pass-phase-shifters) [^2]: [HighPassLowPassPhaseShift-1-.pdf](http://d2xunoxnk3vwmv.cloudfront.net/uploads/HighPassLowPassPhaseShift-1-.pdf) [^3]: [Microwaves 101](https://www.microwaves101.com/encyclopedias/transmission-line-model) [^common_uses]: [Robabeh's Thesis](High%20Resolution%20Integrated%20Passive%20Phase%20Shifters%20for%20Future%20Wireless%20Communications.md)